相依风险模型中破产概率的渐近性与统计分析 英文版PDF电子书下载

Preface 1

Chapter 1 Introduction 1

1.1 Risk process and ruin probabilities 4

1.2 C1aim size distributions and claim arrival process 7

1.2.1 Claim size and heavy-tailed or light-tailed distributions 7

1.2.2 The arrival process 10

1.3 The Cramér-Lundberg Estimate 12

Chapter 2 Risk Model with no Interest Rate 17

2.1 Veraverbeke’s theorem 17

2.2 Infinite-time ruin probabilities in two dependent risk models 28

2.2.1 Infinite-time ruin probability with modulated claim sizes 31

2.2.2 Infinite-time ruin probabilitywith NUQD claim sizes 35

2.3 Finite-time ruin probabilities with NLQD inter-arrival times 36

2.4 Supremum of a dependent random walk with subexponential imcrements 53

Chapter 3 Risk Model with Interest Rate 66

3.1 Finite-time ruin probabilities with dominatedly-varying-tailed claim sizes 67

3.1.1 Some existing results in the independence case 67

3.1.2 Asymptotics and uniform asymptotics for finite-time ruin probabilities in the dependence case 69

3.2 Further results on asymptotics and uniform asymptotics for ruin probabilities with dominatedly-varying-tailed claim sizes 84

3.3 Finite-time ruin probabilities with subexponential claim sizes in the dependent compound renewal risk model 93

3.3.1 Compound renewal risk model and dependence structures 93

3.3.2 Finite-time ruin probabilities with subexponential individual claim sizes 97

3.3.3 Simulation study 107

Chapter 4 Discrete-time Risk Model with Insurance and Financial Risks 111

4.1 Randomly weighted sums in the independence case 112

4.1.1 Randomly weighted finite sums 112

4.1.2 Randomly weighted infinite sums 114

4.2 Randomly weighted sums in the dependence case 115

4.2.1 Randomly weighted finite sums with dependent primary random variables 115

4.2.2 Randomly weighted finite sums with dependence between the primary random variable and the random weight 116

4.2.3 Randomly weighted infinite sums with dependent primary random variables 128

Bibliography 141

编后记 148